Magnetic resonance imaging (MRI) is an important diagnostic and imaging technique. MRI techniques are based on the absorption and emission of radio frequency (RF) energy by the nuclei of atoms. Typically, a target is placed in a strong magnetic field that causes the generally disordered and randomly oriented nuclear spins of the atoms to become aligned with the applied magnetic field. One or more RF pulses are transmitted into the target, perturbing the nuclear spins. As the nuclear spins relax to their aligned state, the nuclei emit RF energy that is detected by receiving coils disposed about the target. The received RF energy is processed into a magnetic resonance image of a portion of the target.
By utilizing non-uniform magnetic fields having gradients in each of three spatial dimensions, the location of the emitting nuclei can be spatially encoded so that the target can be imaged in three dimensions (3-D). The three dimensions are commonly two mutually orthogonal directions x and y defined in a plane denoted as a “slice” with a series of slices defined in a third mutually orthogonal direction z. Generally, RF pulses having a range of frequencies are transmitted into the target, and through use of well-known spatial encoding techniques, a set of MRI data is received by each of the receiver coils for each slice in the target.
MRI data provides a representation of the MRI image in the frequency domain, often called k-space domain, where kx and ky are the spatial frequency variables in the x and y directions having units of cycles per unit distance. An image of the slice of the target typically is obtained by performing an inverse Fourier transformation of the k-space MRI data. In MRI systems having multiple receiver coils (parallel MRI), an image is reconstructed from each receiver coil, and a final image is a combination of the images from each coil. Multiple receiver coil systems can be used to achieve high spatial and temporal resolution, to suppress image artifacts, and to reduce MRI scan time.
MRI data can be acquired at the appropriate Nyquist sampling rate to avoid artifacts in the final image caused by aliasing. However, sampling at the Nyquist rate is time consuming, which can prevent the imaging of targets that move, such as a beating heart. The reduction in the number of k-space samples steps to the Nyquist sampling rate is known as undersampling and is characterized by a reduction factor, R. Various undersampling strategies are possible. Non-uniform undersampling, also called variable-density undersampling, generally more densely samples a central region of k-space, and more sparsely samples an outer region. The undersampling results in certain data in k-space not being acquired, and therefore not available for image reconstruction. Thus, images reconstructed from undersampled data with standard methods have aliasing or other artifacts.
Multi-image MRI encompasses numerous important healthcare applications that acquire sets of images. Image sets from applications such as diffusion tensor imaging (DTI), which acquires diffusion weighted images in multiple directions, flow velocity imaging, dynamic contrast enhanced (DCE) imaging of tumors and perfusion, and cardiac motion are all examples of this multi-image class. DTI is an MRI technique that enables the measurement of the restricted diffusion of water in tissue through application of diffusion gradients (i.e. magnetic field variations in the MRI magnet) in at least 6 directions. A tensor (i.e. a symmetric positive definite 3×3 matrix) can be calculated that describes the 3-D shape of diffusion of water in the tissue. DTI is in widespread use for clinical indications and for study of the brain and heart and other applications. DCE is an MRI technique that probes the physiology of an organ or an area of interest over time. DCE MR imaging is used to track changes over time in an object of interest by acquiring a series of images. In this process, a contrast agent is injected into the body, or an endogenous contrast is used as in spin-labeling and images are acquired over time to track the uptake and washout patterns of an area of interest. Rapid acquisitions are required to track the quickly changing contrast in the object. One application of DCE MRI is myocardial perfusion, which is an important tool for assessing coronary artery disease.
It takes a relatively long time to acquire full data in k-space for each time frame without tradeoffs in spatial and temporal resolution. Additionally, the acquisition of full data for different diffusion directions takes a long time and limits the use of the technique. What is needed, therefore, is a method and a system for reducing the acquisition time of imaging data and/or for enabling improved spatial or temporal resolution or signal-to-noise ratio without an increase in acquisition time while maintaining the diagnostic quality of the image.